An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues

• Published in: Journal of Agricultural, Biological and Environmental Statistics
• Main Authors: Van Helsdingen, Alec B.M., Marques, Tiago A., Jones-Todd, Charlotte M.
• Other Authors: University of St Andrews.School of Mathematics and Statistics, University of St Andrews.Centre for Research into Ecological & Environmental Modelling, University of St Andrews.Statistics
• Format: Article in Journal/Newspaper
• Language: English
• Published: 2024
• Subjects: Overdispersion; Point patterns; Self-excitement; Sperm whale; Underdispersion; Statistics and Probability; General Environmental Science; Agricultural and Biological Sciences (miscellaneous); General Agricultural and Biological Sciences; Statistics; Probability and Uncertainty; Applied Mathematics; DAS; Hawkes; Hawkes Point; Marsden
• Online Access: https://hdl.handle.net/10023/29870; https://doi.org/10.1007/s13253-024-00626-w

Funding: TAM time covered by ACCURATE, funded by the US Navy Living Marine Resources program (contract no. N3943019C2176). TAM thanks partial support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UIDB/00006/2020). This work was supported by Marsden Fund proposal UOA 3723517 and Asian Office of Aerospace Research & Development grant FA2386-21-1-4028. A Hawkes point process describes self-exciting behaviour where event arrivals are triggered by historic events. These models are increasingly becoming a popular choice in analysing event-type data. Like all other inhomogeneous Poisson point processes, the waiting time between events in a Hawkes process is derived from an exponential distribution with mean one. However, as with many ecological and environmental data, this is an unrealistic assumption. We, therefore, extend and generalise the Hawkes process to account for potential under- or overdispersion in the waiting times between events by assuming the Weibull distribution as the foundation of the waiting times. We apply this model to the acoustic cue production times of sperm whales and show that our Weibull–Hawkes model better captures the inherent underdispersion in the interarrival times of echolocation clicks emitted by these whales. Peer reviewed